{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1ea79b53-3ec2-4783-aa44-9cb9a0e2c43c",
   "metadata": {},
   "source": [
    "Chapter 20\n",
    "# 有向图邻接矩阵\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f34e773-51a9-4b91-bca5-f0bc12fbe8c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "67b53379-bbec-4769-b04a-3912aac970b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.DiGraph()\n",
    "# 创建有向图的实例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1bd402bb-e445-4f8d-9758-78215ea8378e",
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_nodes_from(['a', 'b', 'c', 'd', 'e', 'f'])\n",
    "# 添加多个顶点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "58d29c53-bea0-469b-b5b1-65d306f2b340",
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_edges_from([('a','c'),('a','f'),\n",
    "                  ('b','a'),('b','e'),\n",
    "                  ('c','b'),('c','d'),\n",
    "                  ('d','a'),('d','e'),\n",
    "                  ('e','f'),('e','c'),\n",
    "                  ('f','c'),('f','b')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5106dbdf-296f-465f-8143-908d1dba03c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 城市具体位置\n",
    "\n",
    "pos = {'a':(50.6463,6.5692),\n",
    "       'b':(70.3019,41.0777),\n",
    "       'c':(35.6363,36.0673),\n",
    "       'd':(6.8205,16.8171),\n",
    "       'e':(26.1044,68.8277),\n",
    "       'f':(59.1871,69.6398)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a5488307-c29f-4679-a226-be46f22adfd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# 可视化\n",
    "plt.figure(figsize = (6,6))\n",
    "nx.draw_networkx(G, \n",
    "                 pos = pos,\n",
    "                 node_size = 180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d1d6a5be-b24a-4efc-93b3-0f1906f81141",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1, 0, 0, 1],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [0, 1, 0, 1, 0, 0],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [0, 0, 1, 0, 0, 1],\n",
       "       [0, 1, 1, 0, 0, 0]], dtype=int32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 邻接矩阵\n",
    "A = nx.adjacency_matrix(G).todense()\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b55f15e0-53b5-4cd6-a648-2717fa208779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pbgAAbIgOGgDgCExxAwBgQ6ziBgAAlqODBgA4gmENNAUaAOAMpk1xU6ABAI5gWoHmPWgAAGyIDhoA4AiGNdAUaACAMzDFDQAALEcHDQBwBMMaaAo0AMAZmOIGAACWo4MGADiCYQ00BRoA4AxMcQMAAMvRQQMAHMGwBpoCDQBwBtOmuG1VoE8WL7Y6hKiLjzXrhjuNvM1h4vNaMnOsI82w+sx70AAA2JGtOuiaUwGrQ4ia06+uvb0nWRxJdJ3upkwaa8nM8TZ9rE3KO1qzBUxxAwBgQ4bVZ6a4AQCwIzpoAIAjMMUNAIANGVafmeIGAMCO6KABAI7AFDcAADZkWoFmihsAABuigwYAOIJhDTQFGgDgDKZNcVOgAQCOYFh95j1oAADsiA4aAOAITHEDAGBDhtVnprgBALAjOmgAgCO4DWuhKdAAAEcwrD4zxQ0AgB3RQQMAHMG0Vdx00AAAR3C7wrc11eLFi5Weni6v16usrCzt2LHjnMcfO3ZMkyZNUocOHeTxeHT11Vdr48aNTbomHTQAwBGs6qDXrl2r3NxcLVmyRFlZWVq4cKGGDRumAwcOqF27dg2Or6ur00033aR27dpp3bp1Sk1N1f/+7/+qbdu2TbouBRoAgHNYsGCB7rnnHo0fP16StGTJEm3YsEErVqzQzJkzGxy/YsUKHT16VO+//75iY2MlSenp6U2+LlPcAABHcLnCt9XW1qqqqipkq62tbXDNuro67dy5Uzk5OcF9brdbOTk5KioqOmOc69evV3Z2tiZNmqSUlBT16NFDTz31lOrr65uUr9EFes3qP+iWm27QgD49ddedP9XePXusDimihvTtpHULJ+rw5idVs3uRhg/NtDqkqGGsGeuWzoS8XWH8x+fzKSEhIWTz+XwNrlleXq76+nqlpKSE7E9JSVFpaekZ4zx8+LDWrVun+vp6bdy4UbNnz9b8+fP1xBNPNClfYwv0pj9t1LPzfJp4/yStefUNZWR00X0TJ6iiosLq0CKmVbxHew9+rgd9a60OJaoYa3OYONaSuXlfiLy8PB0/fjxky8vLC8u5/X6/2rVrp6VLl6pfv34aPXq0Hn30US1ZsqRJ5zG2QK9a+TuNuuNnGjHydnXq3Fmz8ufK6/Xqzddfszq0iNm8dZ/mFryl9e+0vFfW58JYm8PEsZbMyTucq7g9Ho/atGkTsnk8ngbXTE5OVkxMjMrKykL2l5WVqX379meMs0OHDrr66qsVExMT3Ne1a1eVlpaqrq6u8fk2+sgW5FRdnfbv+0iDsgcH97ndbg0aNFh7PtxtYWQIN8baHKaOtUl5u1yusG2NFRcXp379+qmwsDC4z+/3q7CwUNnZ2Wd8zJAhQ3To0CH5/f7gvoMHD6pDhw6Ki4tr9LWbVaB9Pp9WrFjRYP+KFSv029/+tjmnjKrKY5Wqr69XUlJSyP6kpCSVl5dbFBUigbE2h6ljbWre0ZSbm6tly5Zp5cqV2r9/v+677z5VV1cHV3WPHTs2ZHr8vvvu09GjRzV16lQdPHhQGzZs0FNPPaVJkyY16brN+pjViy++qNWrVzfY3717d915552aMWPGOR9fW1t7xtVyAACcjVVfJDZ69GgdOXJEc+bMUWlpqXr37q1NmzYFF46VlJTI7f6+301LS9Pbb7+tadOmKTMzU6mpqZo6dep5a+P/1awCXVpaqg4dOjTYf9lll+nLL7887+N9Pp/mzp3bnEuHRWLbRMXExDRYQFFRUaHk5GSLokIkMNbmMHWsTcrbyl+zmjx5siZPnnzG/7Zly5YG+7Kzs7Vt27YLumazprjT0tK0devWBvu3bt2qyy+//LyPP9PquWiKjYtT127dtX3b959h8/v92r69SJm9+kQ1FkQWY20OU8fa1LxN0KwO+p577tGDDz6oU6dO6YYbbpAkFRYW6uGHH9avf/3r8z7e4/GccbVcNN09brxmPzJD3bv3UI+emXpl1UrV1NRoxMhRlsYVSa3i49Qp7bLg3+mpScq8OlWVVSf0j9JKCyOLLMaasW7JYy2Zk7dhv5XRvAL90EMPqaKiQvfff39wybjX69WMGTPC9jmySLv5lltVefSoChY9r/LyI8ro0lUFLy5XUgubEvpnfbtdoc3Lpwb/njf9dknSqvXbdG/+K1aFFXGMNWPdksdaMidv037NyhUIBALNffA333yj/fv3Kz4+XlddddUFdcUul0s1p5odiuPEx353o3l7N21Vn9OdLF4sSUaNtWTmeJs+1iblHR/r0gWUkkb76cu7wnauV/+1b9jOFSkX9GMZrVu31oABA8IVCwAA+H/4NSsAgCNYuYrbChRoAIAjmFWeDf2qTwAA7I4OGgDgCKat4qZAAwAcwW1WfWaKGwAAO6KDBgA4AlPcAADYkGH1mSluAADsiA4aAOAITHEDAGBDpq3ipkADABzBtA6a96ABALAhOmgAgCOY1T9ToAEADmHar1kxxQ0AgA3RQQMAHMGwBpoCDQBwBlZxAwAAy9FBAwAcwbAGmgINAHAGVnEDAADL0UEDABzBsAbaXgU6Ptaw//uSThYvtjoES5g41pKZ423qWJuadySZtorbVgUaAICzMe09WVsVaG/vSVaHEDWnO6maUwGLI4mu010Febd8p3M26XktmfncZrYgMmxVoAEAOBumuAEAsCG3WfXZuCl9AAAcgQ4aAOAIpnXQFGgAgCOY9h40U9wAANgQHTQAwBGY4gYAwIYMm+FmihsAADuigwYAOIJpPzdJgQYAOIJpU74UaACAIxjWQBv3ggQAAEeggwYAOALvQQMAYEOG1WemuAEAsCM6aACAI/BNYgAA2JBp70EzxQ0AgA3RQQMAHMGwBpoCDQBwBtPeg2aKGwAAG6KDBgA4gktmtdAUaACAIzDFbYghfTtp3cKJOrz5SdXsXqThQzOtDilq1qz+g2656QYN6NNTd935U+3ds8fqkCLOxJwl8/Lmed2yx9rtCt/mBMYW6FbxHu09+Lke9K21OpSo2vSnjXp2nk8T75+kNa++oYyMLrpv4gRVVFRYHVrEmJizZGbePK/NGWsTGFugN2/dp7kFb2n9Oy3vVea5rFr5O42642caMfJ2dercWbPy58rr9erN11+zOrSIMTFnycy8eV637LF2uVxh25zA2AJtolN1ddq/7yMNyh4c3Od2uzVo0GDt+XC3hZFFjok5S+bmbSKTxtq0Ke5GLxLLzc1t9EkXLFhwzv9eW1ur2traRp8P4VF5rFL19fVKSkoK2Z+UlKRPPz1sUVSRZWLOkrl5m4ixbrkaXaB37w59JbZr1y59++23ysjIkCQdPHhQMTEx6tev33nP5fP5NHfu3CaGCgAwmUNmpsOm0QX6nXfeCf77ggULdMkll2jlypVKTEyUJFVWVmr8+PH64Q9/eN5z5eXlNejIExISGhsKmimxbaJiYmIaLBypqKhQcnKyRVFFlok5S+bmbSKTxpofy2iE+fPny+fzBYuzJCUmJuqJJ57Q/Pnzz/t4j8ejNm3ahGyIvNi4OHXt1l3btxUF9/n9fm3fXqTMXn0sjCxyTMxZMjdvEzHWLVezCnRVVZWOHDnSYP+RI0f09ddfX3BQ0dAqPk6ZV6cq8+pUSVJ6apIyr05VWvvE8zzS2e4eN16vr/uj1r/5hg5/8omeeOw3qqmp0YiRo6wOLWJMzFkyM2+e1y17rK1cJLZ48WKlp6fL6/UqKytLO3bsaNTj1qxZI5fLpREjRjT5ms36JrGRI0dq/Pjxmj9/vgYOHChJ2r59ux566CGNGuWMG6Jvtyu0efnU4N/zpt8uSVq1fpvuzX/FqrAi7uZbblXl0aMqWPS8ysuPKKNLVxW8uFxJLWwq7J+ZmLNkZt48r1v2WFs1w7127Vrl5uZqyZIlysrK0sKFCzVs2DAdOHBA7dq1O+vjPvvsM02fPr1Rb/2eiSsQCASa+qATJ05o+vTpWrFihU6dOiVJuuiiizRhwgQ988wzatWqVdMDcbnk7T2pyY9zqpPFiyVJNaea/L/f0eJjv3uGkXfLdzpnk57XkpnP7fhYl5pRSprsP7Z+GrZz3dv/8gafJvJ4PPJ4PA2OzcrK0oABA7Ro0SJJ372FkJaWpilTpmjmzJlnPH99fb2uvfZa/du//Zv++te/6tixY3rzzTebFGOzprgvvvhiFRQUqKKiQrt379bu3bt19OhRFRQUNKs4AwBwPm65wrb5fD4lJCSEbD6fr8E16+rqtHPnTuXk5Hwfh9utnJwcFRUVNTj+tMcee0zt2rXThAkTmp3vBf1YRqtWrZSZac533QIArBPOKe4zfZroTN1zeXm56uvrlZKSErI/JSVFH3/88RnP/d577+mll15ScXHxBcXIr1kBABwhnN8Adrbp7Av19ddf6+6779ayZcsu+GNuFGgAAM4iOTlZMTExKisrC9lfVlam9u3bNzj+k08+0Weffabhw4cH9/n9fknfrdU6cOCAOnXq1Khr813cAABHcLtcYdsaKy4uTv369VNhYWFwn9/vV2FhobKzsxsc36VLF+3du1fFxcXB7bbbbtP111+v4uJipaWlNfradNAAAEew6mNWubm5GjdunPr376+BAwdq4cKFqq6u1vjx4yVJY8eOVWpqqnw+n7xer3r06BHy+LZt20pSg/3nQ4EGAOAcRo8erSNHjmjOnDkqLS1V7969tWnTpuDCsZKSErnd4Z+QpkADABzByu/injx5siZPnnzG/7Zly5ZzPvbll19u1jUp0AAARzDstzJYJAYAgB3RQQMAHMG0jpICDQBwBJdhc9ymvSABAMAR6KABAI5gVv9MgQYAOISVH7OyAgUaAOAIZpVn3oMGAMCW6KABAI5g2Aw3BRoA4Ax8zAoAAFiODhoA4AimdZQUaACAIzDFDQAALEcHDQBwBLP6Z8kVCAQCVgchmTd1AQAtSTRKyboPvwzbue7o1SFs54oUprgBALAhW01x15yyRTMfFfGx380YmJSz9H3e3t6TLI4kuk4WL5Zk1nhzj5tzj5++vyPNtI7SVgUaAICzMe2tUAo0AMARzCrP5s0YAADgCHTQAABHMGyGmwINAHAGt2GT3ExxAwBgQ3TQAABHYIobAAAbcjHFDQAArEYHDQBwBKa4AQCwIVZxAwAAy9FBAwAcgSluAABsiAINAIAN8TErAABgOTpoAIAjuM1qoCnQAABnYIobAABYjg4aAOAIrOIGAMCGmOIGAACWo4MGADgCq7gBALAhprgNsmb1H3TLTTdoQJ+euuvOn2rvnj1WhxQVpuU9pG8nrVs4UYc3P6ma3Ys0fGim1SFFjWljLZmZs8n3eEtmbIHe9KeNenaeTxPvn6Q1r76hjIwuum/iBFVUVFgdWkSZmHereI/2HvxcD/rWWh1KVJk41ibmLJlzj7tc4ducwNgCvWrl7zTqjp9pxMjb1alzZ83Knyuv16s3X3/N6tAiysS8N2/dp7kFb2n9Oy2/k/pnJo61iTlL5tzjrjBuTtDsAv3Xv/5Vv/jFL5Sdna3PP/9ckrRq1Sq99957YQsuUk7V1Wn/vo80KHtwcJ/b7dagQYO158PdFkYWWabmbSITx9rEnE3jdrnCtjlBswr0a6+9pmHDhik+Pl67d+9WbW2tJOn48eN66qmnzvv42tpaVVVVhWzRVHmsUvX19UpKSgrZn5SUpPLy8qjGEk2m5m0iE8faxJzRsjWrQD/xxBNasmSJli1bptjY2OD+IUOGaNeuXed9vM/nU0JCQsgGAMC5MMXdCAcOHNC1117bYH9CQoKOHTt23sfn5eXp+PHjIVs0JbZNVExMTIOFIxUVFUpOTo5qLNFkat4mMnGsTczZOIZV6GYV6Pbt2+vQoUMN9r/33nvq2LHjeR/v8XjUpk2bkC2aYuPi1LVbd23fVhTc5/f7tX17kTJ79YlqLNFkat4mMnGsTcwZLVuzvqjknnvu0dSpU7VixQq5XC598cUXKioq0vTp0zV79uxwxxgRd48br9mPzFD37j3Uo2emXlm1UjU1NRoxcpTVoUWUiXm3io9Tp7TLgn+npyYp8+pUVVad0D9KKy2MLLJMHGsTc5bMucdN+6KSZhXomTNnyu/368Ybb9SJEyd07bXXyuPxaPr06ZoyZUq4Y4yIm2+5VZVHj6pg0fMqLz+ijC5dVfDiciW18KkwE/Pu2+0KbV4+Nfj3vOm3S5JWrd+me/NfsSqsiDNxrE3MWTLnHnfI4uuwcQUCgUBzH1xXV6dDhw7pm2++Ubdu3dS6devmB+JyqeZUs0NxnPjY7+40k3KWvs/b23uSxZFE18nixZLMGm/ucXPu8ZPFi3UBpaTRdhwO33qlgR3tvzj5gr6LOy4uTt26dQtXLAAAnJVhDTQ/lgEAcAjDKrSxX/UJAICd0UEDAByBVdwAANiQaau4KdAAAEcwrD7zHjQAAHZEBw0AcAbDWmgKNADAEUxbJMYUNwAA57F48WKlp6fL6/UqKytLO3bsOOuxy5Yt0w9/+EMlJiYqMTFROTk55zz+bCjQAABHcLnCtzXF2rVrlZubq/z8fO3atUu9evXSsGHD9NVXX53x+C1btmjMmDF65513VFRUpLS0NP3oRz/S559/3rR8L+S7uMOJ7+I2g4nfUyzxXdwmMfEej9Z3cX9Y8nXYztUlJU61tbUh+zwejzweT4Njs7KyNGDAAC1atEjSdz9jmpaWpilTpmjmzJnnvVZ9fb0SExO1aNEijR07ttEx0kEDAIzj8/mUkJAQsvl8vgbH1dXVaefOncrJyQnuc7vdysnJUVFRUYPjz+TEiRM6deqULr300ibFyCIxAIAzhHGNWF5ennJzc0P2nal7Li8vV319vVJSUkL2p6Sk6OOPP27UtWbMmKHLL788pMg3BgUaAOAI4VzFfbbp7HB7+umntWbNGm3ZskVer7dJj6VAAwBwFsnJyYqJiVFZWVnI/rKyMrVv3/6cj3322Wf19NNP67/+67+UmZnZ5GvzHjQAwBGsWMUdFxenfv36qbCwMLjP7/ersLBQ2dnZZ33cvHnz9Pjjj2vTpk3q379/s/KlgwYAOIJVX1OSm5urcePGqX///ho4cKAWLlyo6upqjR8/XpI0duxYpaamBheZ/fa3v9WcOXO0evVqpaenq7S0VJLUunVrtW7dutHXpUADAJzBogo9evRoHTlyRHPmzFFpaal69+6tTZs2BReOlZSUyO3+fkL6hRdeUF1dne64446Q8+Tn5+s3v/lNo69LgQYA4DwmT56syZMnn/G/bdmyJeTvzz77LCzXpEADABzBtO/ipkADAByhqV/R6XSs4gYAwIbooAEAjmBYA22vH8sAADhTNErJ/i+rw3aurh1ahe1ckcIUNwAANmSrKW6TfpbOxJ+kk77/2UVT8zbxHjcpZ8nMvE/nHGms4gYAwIZMeyeUKW4AAGyIDhoA4AiGNdAUaACAQxhWoSnQAABHMG2RGO9BAwBgQ3TQAABHMG0VNwUaAOAIhtVnprgBALAjOmgAgDMY1kJToAEAjsAqbgAAYDk6aACAI7CKGwAAGzKsPjPFDQCAHdFBAwCcwbAWmgINAHAE01ZxU6ABAI5g2iIx3oMGAMCG6KABAI5gWANNgQYAOANT3AAAwHJ00AAAhzCrhTa6g16z+g+65aYbNKBPT91150+1d88eq0OKqCF9O2ndwok6vPlJ1exepOFDM60OKSpMzVsy7x6XzMxZMiNvlyt8mxMYW6A3/Wmjnp3n08T7J2nNq28oI6OL7ps4QRUVFVaHFjGt4j3ae/BzPehba3UoUWVq3ibe4ybmLJmbd0tnbIFetfJ3GnXHzzRi5O3q1LmzZuXPldfr1Zuvv2Z1aBGzees+zS14S+vfaXmvrM/F1LxNvMdNzFkyJ29XGDcnMLJAn6qr0/59H2lQ9uDgPrfbrUGDBmvPh7stjAwIDxPvcRNzlszKmynuM9izZ4/8fn/YLlpbW6uqqqqQLZoqj1Wqvr5eSUlJIfuTkpJUXl4e1ViASDDxHjcxZ8ncvE3QqALdp0+f4EB37Njxgt/X8Pl8SkhICNkAADgXVxj/cYJGFei2bdvq008/lSR99tlnF9xN5+Xl6fjx4yFbNCW2TVRMTEyDFxoVFRVKTk6OaixAJJh4j5uYs2RY3oa9Cd2oAn377bfruuuu05VXXimXy6X+/furY8eOZ9waw+PxqE2bNiFbNMXGxalrt+7avq0ouM/v92v79iJl9uoT1ViASDDxHjcxZ8msvA2rz437opKlS5dq1KhROnTokB544AHdc889uuSSSyIdW0TdPW68Zj8yQ92791CPnpl6ZdVK1dTUaMTIUVaHFjGt4uPUKe2y4N/pqUnKvDpVlVUn9I/SSgsjiyxT8zbxHjcxZ8ncvFu6Rn+T2M033yxJ2rlzp6ZOner4An3zLbeq8uhRFSx6XuXlR5TRpasKXlyupJY2JfRP+na7QpuXTw3+PW/67ZKkVeu36d78V6wKK+JMzdvEe9zEnCVz8nbK6utwcQUCgYDVQUiSy+VSzSlbhBIV8bHf3Wne3pMsjiS6ThYvlmRu3ibe4yblLJmZd3ysS9EoJUe+/jZs57rsEvt/07WRn4MGAMDu7P8SAgAAyTmru8KEAg0AcATD6jNT3AAA2BEdNADAEUxbxU2BBgA4glO+ojNcmOIGAMCG6KABAI5g2hQ3HTQAADZEBw0AcAQ6aAAAYDk6aACAI5i2ipsCDQBwBKa4AQCA5eigAQCOYFgDTYEGADiEYRWaKW4AAGyIDhoA4Ais4gYAwIZYxQ0AACxHBw0AcATDGmgKNADAIQyr0ExxAwAcwRXGf5pq8eLFSk9Pl9frVVZWlnbs2HHO41999VV16dJFXq9XPXv21MaNG5t8TQo0AADnsHbtWuXm5io/P1+7du1Sr169NGzYMH311VdnPP7999/XmDFjNGHCBO3evVsjRozQiBEj9Le//a1J13UFAoFAOBK4UC7TlucBQAsSjVJy8tvwnctVX6va2tqQfR6PRx6Pp8GxWVlZGjBggBYtWiRJ8vv9SktL05QpUzRz5swGx48ePVrV1dV66623gvsGDRqk3r17a8mSJY2O0TYddCAQsGQ7efKk8vPzdfLkSctiIGfyJmfydnre0eC9KHybz+dTQkJCyObz+Rpcs66uTjt37lROTk5wn9vtVk5OjoqKis4YZ1FRUcjxkjRs2LCzHn82tumgrVJVVaWEhAQdP35cbdq0sTqcqDAxZ8nMvE3MWSJv0/JujtraxnXQX3zxhVJTU/X+++8rOzs7uP/hhx/Wu+++q+3btzc4d1xcnFauXKkxY8YE9xUUFGju3LkqKytrdIys4gYAGOds09l2YpspbgAA7CY5OVkxMTENOt+ysjK1b9/+jI9p3759k44/Gwo0AABnERcXp379+qmwsDC4z+/3q7CwMGTK+59lZ2eHHC9Jf/7zn896/NkYP8Xt8XiUn59v+6mOcDIxZ8nMvE3MWSJv0/KOtNzcXI0bN079+/fXwIEDtXDhQlVXV2v8+PGSpLFjxyo1NTW4yGzq1Km67rrrNH/+fP34xz/WmjVr9MEHH2jp0qVNuq7xi8QAADifRYsW6ZlnnlFpaal69+6t559/XllZWZKkoUOHKj09XS+//HLw+FdffVWzZs3SZ599pquuukrz5s3Trbfe2qRrUqABALAh3oMGAMCGKNAAANgQBRoAABuiQBtk6NChevDBB60OAxbiHmi5AoGA7r33Xl166aVyuVwqLi62OiRcIOM/ZgUALcGmTZv08ssva8uWLerYsaOSk5OtDgkXiAINAC3AJ598og4dOmjw4MFWh4IwMXaKe9OmTbrmmmvUtm1bJSUl6Sc/+Yk++eQTq8OKuG+//VaTJ09WQkKCkpOTNXv27Kj9Eo2V/H6/5s2bp86dO8vj8ehf/uVf9OSTT1odVkRVV1dr7Nixat26tTp06KD58+dbHVLE+f1++Xw+XXnllYqPj1evXr20bt06q8OKuH/913/VlClTVFJSIpfLpfT0dKtDQhgYW6Crq6uVm5urDz74QIWFhXK73Ro5cqT8fr/VoUXUypUrddFFF2nHjh167rnntGDBAi1fvtzqsCIuLy9PTz/9tGbPnq19+/Zp9erVSklJsTqsiHrooYf07rvv6j//8z+1efNmbdmyRbt27bI6rIjy+Xz6/e9/ryVLluijjz7StGnT9Itf/ELvvvuu1aFF1HPPPafHHntMP/jBD/Tll1/qf/7nf6wOCeEQQCAQCASOHDkSkBTYu3ev1aFEzHXXXRfo2rVrwO/3B/fNmDEj0LVrVwujiryqqqqAx+MJLFu2zOpQoubrr78OxMXFBf74xz8G91VUVATi4+MDU6dOtS6wCDp58mTg4osvDrz//vsh+ydMmBAYM2aMRVFFz7//+78HrrjiCqvDQBgZ20H//e9/15gxY9SxY0e1adMmOCVUUlJibWARNmjQILlcruDf2dnZ+vvf/676+noLo4qs/fv3q7a2VjfeeKPVoUTNJ598orq6uuBXEUrSpZdeqoyMDAujiqxDhw7pxIkTuummm9S6devg9vvf/96It6/Q8hi7SGz48OG64oortGzZMl1++eXy+/3q0aOH6urqrA4NYRYfH291CIiCb775RpK0YcMGpaamhvw3fjwCTmRkB11RUaEDBw5o1qxZuvHGG9W1a1dVVlZaHVZUbN++PeTvbdu26aqrrlJMTIxFEUXeVVddpfj4+AY//9aSderUSbGxsSHjXVlZqYMHD1oYVWR169ZNHo9HJSUl6ty5c8iWlpZmdXhAkxnZQScmJiopKUlLly5Vhw4dVFJSopkzZ1odVlSUlJQoNzdXEydO1K5du/Qf//EfLX51r9fr1YwZM/Twww8rLi5OQ4YM0ZEjR/TRRx9pwoQJVocXEa1bt9aECRP00EMPKSkpSe3atdOjjz4qt7vlvia/5JJLNH36dE2bNk1+v1/XXHONjh8/rq1bt6pNmzYaN26c1SECTWJkgXa73VqzZo0eeOAB9ejRQxkZGXr++ec1dOhQq0OLuLFjx6qmpkYDBw5UTEyMpk6dqnvvvdfqsCJu9uzZuuiiizRnzhx98cUX6tChg371q19ZHVZEPfPMM/rmm280fPhwXXLJJfr1r3+t48ePWx1WRD3++OO67LLL5PP5dPjwYbVt21Z9+/bVI488YnVoQJPxc5MAANhQy53vAgDAwSjQAADYEAUaAAAbokADAGBDFGgAAGyIAg0AgA1RoAEAsCEKNAAANkSBBgDAhijQAADYEAUaAAAb+v8BhoABfXPto5AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A, cmap = 'Blues', \n",
    "            annot = True, fmt = '.0f',\n",
    "            xticklabels = list(G.nodes), \n",
    "            yticklabels = list(G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('有向图邻接矩阵.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "413a4467-fd1c-460c-8e1f-09998e8407c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2, 1, 1, 0, 0],\n",
       "       [0, 0, 2, 0, 0, 2],\n",
       "       [2, 0, 0, 0, 2, 0],\n",
       "       [0, 0, 2, 0, 0, 2],\n",
       "       [0, 2, 1, 1, 0, 0],\n",
       "       [1, 1, 0, 1, 1, 0]], dtype=int32)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6ce96fcd-f964-4f66-8945-88769b3a06e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 1, 0, 1, 3, 0],\n",
       "       [0, 4, 2, 2, 0, 0],\n",
       "       [0, 0, 4, 0, 0, 4],\n",
       "       [0, 4, 2, 2, 0, 0],\n",
       "       [3, 1, 0, 1, 3, 0],\n",
       "       [2, 0, 2, 0, 2, 2]], dtype=int32)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "23599fb1-0d73-4122-a549-1b54e30d9b02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 0, 6, 0, 2, 6],\n",
       "       [6, 2, 0, 2, 6, 0],\n",
       "       [0, 8, 4, 4, 0, 0],\n",
       "       [6, 2, 0, 2, 6, 0],\n",
       "       [2, 0, 6, 0, 2, 6],\n",
       "       [0, 4, 6, 2, 0, 4]], dtype=int32)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A @ A @ A @ A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6820ad0-b318-4bb8-af8d-a05b2111586a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a172ed9-e863-4c35-86a6-8720105f077e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a7ea3ebb-ba4e-4cbb-9746-f692cde07da3",
   "metadata": {},
   "source": [
    "## 每行元素之和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bc1b9e28-c40c-48e6-a9b2-50b9a0e18e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "T_T = A /  A.sum(axis=1)[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "56172080-671b-4c44-af1f-9217151ff560",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0. , 0. , 0.5, 0. , 0. , 0.5],\n",
       "       [0.5, 0. , 0. , 0. , 0.5, 0. ],\n",
       "       [0. , 0.5, 0. , 0.5, 0. , 0. ],\n",
       "       [0.5, 0. , 0. , 0. , 0.5, 0. ],\n",
       "       [0. , 0. , 0.5, 0. , 0. , 0.5],\n",
       "       [0. , 0.5, 0.5, 0. , 0. , 0. ]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T_T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "51032f6b-560b-4696-9b38-3e42e8f81101",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(T_T, cmap = 'Blues', \n",
    "            annot = True, fmt = '.1f',\n",
    "            xticklabels = list(G.nodes), \n",
    "            yticklabels = list(G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('转移矩阵，每行元素之和为1.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e2cf8ff2-9f48-4e54-8066-2ff3ad255272",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "dda09f11-40a1-4140-b131-aa55ee808842",
   "metadata": {},
   "source": [
    "## 每列元素之和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "da4b75f8-7e39-4451-b3ae-69ddfa49a6d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_T = A.T\n",
    "T = A_T /  A_T.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "7acd2af3-891c-4d1a-8299-4414e257b06c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(T, cmap = 'Blues', \n",
    "            annot = True, fmt = '.1f',\n",
    "            xticklabels = list(G.nodes), \n",
    "            yticklabels = list(G.nodes),\n",
    "            linecolor = 'k', square = True,\n",
    "            linewidths = 0.2)\n",
    "plt.savefig('转移矩阵，每列元素之和为1.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "86748b02-073d-4418-9b54-5e0cefe2b3fb",
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       "array([[0.  , 0.  , 0.5 , 0.  , 0.  , 0.25],\n",
       "       [0.5 , 0.  , 0.  , 0.  , 0.5 , 0.25],\n",
       "       [0.25, 0.5 , 0.  , 0.5 , 0.25, 0.  ],\n",
       "       [0.25, 0.  , 0.  , 0.  , 0.25, 0.25],\n",
       "       [0.  , 0.  , 0.5 , 0.  , 0.  , 0.25],\n",
       "       [0.  , 0.5 , 0.  , 0.5 , 0.  , 0.  ]])"
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    "T @ T"
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   "execution_count": 48,
   "id": "0b31acfa-2572-4d61-9d41-077e699019c2",
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   "outputs": [
    {
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       "array([[0.375, 0.   , 0.   , 0.   , 0.375, 0.25 ],\n",
       "       [0.125, 0.5  , 0.   , 0.5  , 0.125, 0.   ],\n",
       "       [0.   , 0.25 , 0.5  , 0.25 , 0.   , 0.25 ],\n",
       "       [0.125, 0.25 , 0.   , 0.25 , 0.125, 0.   ],\n",
       "       [0.375, 0.   , 0.   , 0.   , 0.375, 0.25 ],\n",
       "       [0.   , 0.   , 0.5  , 0.   , 0.   , 0.25 ]])"
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     "execution_count": 48,
     "metadata": {},
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   "source": [
    "T @ T @ T"
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   "execution_count": 49,
   "id": "b6e06898-a3b5-4571-a982-7a2e09dd4ab5",
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   "outputs": [
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       "       [0.   , 0.125, 0.5  , 0.125, 0.   , 0.25 ],\n",
       "       [0.375, 0.   , 0.25 , 0.   , 0.375, 0.375],\n",
       "       [0.   , 0.125, 0.25 , 0.125, 0.   , 0.125],\n",
       "       [0.125, 0.375, 0.   , 0.375, 0.125, 0.   ],\n",
       "       [0.375, 0.   , 0.   , 0.   , 0.375, 0.25 ]])"
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     "execution_count": 49,
     "metadata": {},
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   "source": [
    "T @ T @ T @ T"
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